# The Empirical Limits of Gyrochronology

**Authors:** Luke G. Bouma, Elsa K. Palumbo, Lynne A. Hillenbrand  
**arXiv:** [2303.08830](https://arxiv.org/abs/2303.08830)  
**Date:** 2023-03-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2303.08830v1/

## Key points

- Stellar ages are important for understanding the evolution of planets, stars, and galaxies.
- Gyrochronology is an empirical method to determine stellar age using a star's spin-down as a clock.
- Bouma et al. present an interpolation-based gyrochronology framework that reproduces time- and mass-dependent spin-down rates implied by the latest open cluster data while also matching the rate at which the dispersion in initial stellar rotation periods decreases as stars age.
- The study finds that uncertainty in determining stellar age varies strongly with both stellar mass and age.
- For Sun-like stars (5800 K), statistical age uncertainties improve monotonically from $\pm$38% at 0.2 Gyr to $\pm12$% at 2 Gyr due to empirical scatter of cluster rotation sequences combined with the rate of stellar spin-down.
- For low-mass K-dwarfs (4200 K), posteriors are highly asymmetric due to stalled spin-down, and $\pm$1$\sigma$ age uncertainties vary non-monotonically between 10% and 50% over the first few gigayears.
- High-mass K-dwarfs (5000 K) older than 1.5 Gyr yield the most precise ages, with limiting uncertainties currently set by possible changes in the spin-down rate (12% systematic), calibration of absolute age scale (8% systematic), and width of slow sequence (4% statistical).
- Available models did not match observations of open cluster rotation periods, particularly for K-dwarfs, which have stalled rotational rates from 0.7 to 1.4 Gyr.
- Overall, this work clarifies the accuracy and precision limitations of gyrochronology for main-sequence stars using an interpolation-based framework that matches observed data more accurately than previous models.

## Summary

Stellar ages are crucial for understanding the evolution of planets, stars, and galaxies. One empirical method to determine stellar age is gyrochronology, which uses a star's spin-down as a clock. This technique leverages direct measurements of surface rotation periods inferred from photometric modulation induced by spots or faculae. However, the reality of gyrochronology is complicated by effects other than ordinary magnetized braking that alter stellar rotation periods. In this work, Bouma et al. present an interpolation-based gyrochronology framework that reproduces the time- and mass-dependent spin-down rates implied by the latest open cluster data while also matching the rate at which the dispersion in initial stellar rotation periods decreases as stars age. The authors validate their technique for stars with temperatures of 3800-6200 K and ages of 0.08-2.6 gigayears (Gyr) and use it to reexamine the empirical limits of gyrochronology. The study finds that uncertainty in determining stellar age varies strongly with both stellar mass and age. For Sun-like stars (5800 K), statistical age uncertainties improve monotonically from $\pm$38% at 0.2 Gyr to $\pm12$% at 2 Gyr due to empirical scatter of cluster rotation sequences combined with the rate of stellar spin-down. For low-mass K-dwarfs (4200 K), posteriors are highly asymmetric due to stalled spin-down, and $\pm$1$\sigma$ age uncertainties vary non-monotonically between 10% and 50% over the first few gigayears. High-mass K-dwarfs (5000 K) older than 1.5 Gyr yield the most precise ages, with limiting uncertainties currently set by possible changes in the spin-down rate (12% systematic), calibration of absolute age scale (8% systematic), and width of slow sequence (4% statistical). The authors note that available models did not match observations of open cluster rotation periods, particularly for K-dwarfs, which have stalled rotational rates from 0.7 to 1.4 Gyr. Overall, this work clarifies the accuracy and precision limitations of gyrochronology for main-sequence stars using an interpolation-based framework that matches observed data more accurately than previous models.